A number series is given with one term missing. Examine the pattern in 3, 4, 7, ?, 18, 29, 47 and choose the correct alternative that completes the series.

Introduction / Context:
This number series problem is based on a pattern where each term is formed from the previous two. The given series is 3, 4, 7, ?, 18, 29, 47. We need to identify the rule that connects successive terms and then determine the missing value. Such series often use a relation similar to the Fibonacci pattern, where a term is the sum of two preceding terms.

Given Data / Assumptions:
Series: 3, 4, 7, ?, 18, 29, 47.
One middle term is missing between 7 and 18.
The pattern likely uses the sum of previous terms to generate the next one.
The same rule should apply consistently after the missing term as well.

Concept / Approach:
We suspect that each term after the second is the sum of the previous two terms. This is because 3 + 4 = 7, which matches the third term exactly. If this holds, then the next term (the missing one) should be the sum of 4 and 7, the following term should be the sum of that missing term and 7, and so on. This gives us a clear way to reconstruct the entire series.

Step-by-Step Solution:
Check the relation for the third term: 3 + 4 = 7. Assume the pattern is: next term = sum of previous two terms. Missing term should be 4 + 7 = 11. Next term should be 7 + 11 = 18, which matches the given fifth term. Next: 11 + 18 = 29, which matches the sixth term. Next: 18 + 29 = 47, which matches the seventh term. Therefore, the missing term is 11.

Verification / Alternative check:
With the missing term filled in, the full series becomes 3, 4, 7, 11, 18, 29, 47. Every term from the third onward is the sum of the two immediately before it. This pattern is consistent and leaves no contradictions. No other candidate value yields such a smooth and fully consistent Fibonacci-style series when extended.

Why Other Options Are Wrong:
Option A: 8 would give 7 + 8 = 15, which does not match 18, breaking the pattern immediately.
Option B: 9 would give 7 + 9 = 16, again inconsistent with the given 18.
Option D: 12 yields 7 + 12 = 19, which does not equal 18, so the sequence fails.
Option E: 15 would totally disrupt the later terms since 7 + 15 = 22, not 18.

Common Pitfalls:
Candidates sometimes focus on successive differences, which here are 1, 3, ?, 7, 11, 18, and may not immediately reveal a simple pattern. Another pitfall is to overlook the possibility that each term may depend on two earlier terms instead of just one. Recognising Fibonacci-type series is a crucial skill for many competitive exams.

Final Answer:
The value that maintains the sum-of-previous-two-terms pattern is 11, so the correct option is 11.